Question

Write an equation for the exponential function represented in the table and graph below.

Answer 1

Given:

Given that the values of x and y in the table.

We need to determine the equation for the exponential function represented in the table and graph the equation.

Equation for the exponential function:

The general equation for the exponential function is given by

`y=a(b)^x` ------- (1)

Substituting the coordinate (0,6) in equation (1), we get;

`6=a(b)^0`

`6=a`

Thus, the value of a is 6.

Substituting a = 6 in equation (1), we have;

`y=6(b)^x` -------- (2)

Substituting the coordinate (1,12) in equation (2), we get;

`12=6(b)^1`

`12=6b`

`2=b`

Thus, the value of b is 2.

Substituting b = 2 in equation (2), we get;

`y=6(2)^x`

Thus, the equation for the exponential function is
`y=6(2)^x`

The image of the graph of the exponential function is attached below: